labor contract vs. employment contract

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When translating a question for my Wahl-O-Mat series, I came upon two wordings: labor contract and employment contract. When I looked up their definitions in a monolingual dictionary, I wasn't sure if they both have the same meaning.
Can they be used synonymously?

I also found the translations labor agreement and employment agreement. Can you substitute the words "agreement" and "contract" with each other, or is there a change in meaning?

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If you apply for a new job and the job interview has just been over, what kind of agreement do you arrange with your new employer? A labor contract or an employment contract?

In case these two agreements are different things, what is their difference?

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Oh, it's obviously good that I've asked that question. Thanks for your detailed reply!

I wanted to translate Arbeitsvertrag into English and looked it up in an online dictionary.
I got the results: employment agreement, employment contract, labor agreement and labor contract.
When I was about to find out which term would fit the most, I discovered that a labor contract and an employment contract seem to be different things in the English language. In order to learn the definitions of these wordings, I used a monolingual dictionary which defines them as follows:

labor contract [countable] American English
an agreement between a company and a LABOR UNION on pay, conditions etc
Italian journalists, in talks to renew their national labor contract, began a three-day strike.

contract of emˈployment noun (plural contracts of employment) [countable]
a formal document giving the conditions of someone’s job, how much they are paid etc
SYN TERMS OF EMPLOYMENT
Under his contract of employment, he is entitled to six months’ notice.

And the fact that one definition contains the interference of labor unions puzzled me.
I did researches on cnn.com, but they didn't made me smarter.
It seems like unions have so few power (unlike in Germany) that the American business sciences discriminate between to different agreements.

But I still don't know what's the better translation for the question asked in the Wahl-O-Mat...

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From a quick googling I think your Wahl-o-Mat question relates to the use of befristeter Arbeitsvertrag. When I looked at some of the longer examples of usage at www.linguee.de, it seems that fixed-term employment contract is the best translation. The problem in translation is I think specific to the laws of the two countries. Let me give four examples of fixed-term employment contracts in the US.

Thank you very much! I was very confused when I discovered that unions are involved in labor contracts.
Your second example is closest to what the question intended. In the original it is not limited to college student but also to those who have graduated. (But No. 4 also fits quite well.)
While the hire-and-fire policy is pretty common and perceived as standard in the US, it is bitterly despised in Europe (outside the UK). Since Schröder's Hartz reforms, however, companies can fire you after your first six months without given any reasons, plus they can offer you time-limited internships as often as they want. They've been exercising their right very rigidly, for which those companies are very often sharply criticized. They can also hire people from private agencies as often as they want since the reforms, which leads to my next question...

Do you call such work placed by private agencies subcontracted labor? And are those private agencies called temporary employment agency? And what are the slaves workers called that can be hired by companies? Agency workers, contract workers, temporary workers? Which translation is the best fit?